Figure 2 shows not only the time variation of the partial regression coefficients and the adjusted R-squares (Adj. R\(^2\)) for each period but also the number of COVID-19 cases throughout Japan. Figure 2a–d show the results for the morning, afternoon, night, and late-night hours, respectively. The vertical axes indicate the values of each coefficient/variable, and the horizontal axes indicate the date. In particular, the vertical axes for \(a_1, \ldots , a_8\) represent the impact on the mobile population per unit number/distance and that for \(a_c\) represents the constant term. \(a_1,\ldots ,a_8\) represent the coefficients for residential (\(a_1\)), commercial (\(a_2\)), school (\(a_3\)), restaurant (\(a_4\)), retail store (\(a_5\)), service (\(a_6\)), leisure (\(a_7\)), and distance to the central business district (\(a_8\)), respectively. Note that each coefficient corresponds to the impact of each travel purpose on the travel volume. For example, commercial corresponds to commuting, school corresponds to going to school, restaurant corresponds to eating out, and so on. A smaller value of a coefficient after compared to before the COVID-19 pandemic suggests that mobility for the corresponding travel purpose was restrained. The coefficients with solid lines indicate that the median P value was less than 0.05, suggesting that the result was statistically significant. In contrast, the coefficients written in dotted lines are those for which the median P value in all windows was greater than or equal to 0.05, indicating that the results were statistically insignificant. For coefficients that changed positively or negatively during the period, a horizontal line is drawn where the value is zero, and the figure for the number of infected people shows the period when a state of emergency was declared7.
The results are analyzed below. First, the adjusted R\(^2\) values were found to be high for all periods, confirming that the extent of human mobility is well represented by the number of buildings by type. The large drop in adjusted R\(^2\) around New Year’s Day in 2020 may be because of the temporary closure of stores and people returning to their home towns.
Second, we investigated the mobility change in the vicinity of the first state of emergency declaration (April 7–May 25, 2020)—that is, during the first wave of the COVID-19 pandemic, when the absolute values of the partial regression coefficients for most of the features were smaller than those before the pandemic in all periods. This may indicate that the impact of each feature on the mobile population decreased because of the sense of crisis caused by the pandemic or the self-restraint with regard to telecommuting and long-distance travel owing to the declaration of a state of emergency. This result is consistent with the results of a study based on a web-based questionnaire survey15. One notable change during this period is that of “restaurant” in the late-night hours. Before the pandemic, “restaurant” was the feature that strongly influenced the increase in late-night travel, and this was considered to be dominated by drinking establishments. However, the influence of “restaurant” on the increase in travel was significantly reduced due to the self-restraint of night-time business operations following the declaration of the state of emergency. The effect of restaurants in the late-night hours on the mobile population declined with each emergency declaration, even after this period, confirming that the request for shorter business hours due to the state of emergency declarations affected the reduction of the mobile population in the late-night hours. The change in the coefficient of “school” during the morning and afternoon hours began to decrease from a very early stage, unlike the other coefficients. This may reflect the fact that many schools were temporarily closed at an early stage when COVID-19 cases began to be confirmed.
Third, we examined the mobility change from after the first wave to before the third wave (around December 2020). After the first wave subsided and the state of emergency was lifted, the absolute values of the partial regression coefficients for all periods increased, but the magnitude remained smaller than before the pandemic regardless of the number of infected people. This may be attributable to the fact that people became accustomed to refraining from long-distance travel because of the spread of telecommuting and continued practicing voluntary restraint in personal travel. It can also be confirmed that, in the second wave (around July–September 2020), the change in mobility remained smaller than in the first wave. This result is consistent with the findings of existing studies19,20. Note that the variation of the partial regression coefficient and the adjusted R\(^2\) in August may be largely attributable to the summer vacation.
Fourth, we analyzed the mobility change from the third wave to the period after the convergence of the fourth wave (December 2020–June 2021). During this period, the magnitude of the partial regression coefficients for each feature remained smaller than before the pandemic regardless of the number of infected people and whether a state of emergency was declared. For both the third and fourth waves, the absolute values of the partial regression coefficients decreased significantly when the number of infected people reached its peak. In contrast to the first wave, we can confirm that these values immediately return to the same values as before the second wave and remained unchanged regardless of the declaration of a state of emergency. Therefore, while mobility was temporarily greatly suppressed during the peak period, once the number of infected people began to decrease, the population continued to follow a certain degree of voluntary restraint in their mobility regardless of the issuance of state of emergency declarations. This may be because people became accustomed to the state of emergency declarations and the COVID-19 pandemic and because of self-restraint fatigue. The results of this analysis are consistent with a study of inter-prefectural travel change using extensive mobility data from the same period in Japan as in this study18.
Fifth, we examined the mobility change around the fifth wave (after July 2021). Here, the number of infected people was larger than before, but the coefficient change was generally smaller than in the first, third, and fourth waves. Therefore, it can be confirmed that general mobility restrictions during the COVID-19 pandemic were in place during the fifth wave, although the restrictions imposed were not particularly strong. Nevertheless, the decrease in the number of infected people can be attributed to factors such as increased vaccination rates, although further investigation is needed to determine the cause.
Finally, we analyzed the overall changes before and after the COVID-19 pandemic. In this study, the analysis was conducted up to the fifth wave of the COVID-19 pandemic, and the absolute values of the coefficients remained smaller than those before the pandemic for almost all periods and travel purposes. This decrease in the absolute value of the coefficients appears to have been sustained for most of the features regardless of whether a state of emergency was declared. This indicates that the decline in human mobility was well-established in the urban areas of Japan even without legally binding lockdowns. Therefore, it can be concluded that self-restraint was sustained until the middle of the COVID-19 pandemic in urban Japan regardless of the mobility purpose and whether a state of emergency was declared.